All Topics  
Numerical linear algebra

 

 
   Email Print
   Bookmark   Link
 

 

Numerical linear algebra
 
 
  Topics Numerical linear algebra Topic Home

Numerical linear algebra is the study of algorithms for performing linear algebra
Linear algebra

Linear algebra is the branch of mathematics concerned with the study of Euclidean vectors, vector spaces , linear maps , and system of linear equations....
 computations, most notably matrix
Matrix (mathematics)

In mathematics, a matrix is a rectangular array of numbers, as shown at the right. In addition to a number of elementary, entrywise operations such as matrix addition a key notion is matrix multiplication....
 operations, on computer
Computer

A computer is a machine that manipulates Data according to a list of Code .The first devices that resemble modern computers date to the mid-20th century , although the computer concept and various machines similar to computers existed earlier....
s. It is often a fundamental part of engineering
Engineering

Engineering is the discipline and profession of applying Technology and science knowledge and utilizing natural laws and physical resources in order to design and implement materials, structures, machines, devices, systems, and process that safely realize a desired objective and meet specified criteria....
 and computational science
Computational science

Computational science is the field of study concerned with constructing mathematical models and numerical solution techniques and using computers to analyse and solve scientific, social science and engineering problems....
 problems, such as image
Image processing

In electrical engineering and computer science, image processing is any form of signal processing for which the input is an , such as photographs or video frame; the output of image processing can be either an image or a set of characteristics or parameters related to the image....
 and signal processing
Signal processing

Signal processing is the analysis, interpretation, and manipulation of signal . Signals of interest include: audio signal processing, , time-varying measurement values and sensor data, for example biological data such as electrocardiograms, control system signals, telecommunication transmission signals such as radio signals, and many others....
, computational finance
Computational finance

Computational finance or financial engineering is a cross-disciplinary field which relies on computational intelligence, mathematical finance, Numerical analysis and computer simulations to make Trader , hedge and investment decisions, as well as facilitating the risk management of those decisions....
, materials science
Materials science

Materials science or materials engineering is an interdisciplinary field involving the properties of matter and its applications to various areas of science and engineering....
 simulations, structural biology
Structural biology

Structural biology is a branch of molecular biology, biochemistry, and biophysics concerned with the molecular structure of biological macromolecules, especially proteins and nucleic acids, how they acquire the structures they have, and how alterations in their structures affect their function....
, data mining
Data mining

Data mining is the process of extracting hidden patterns from data. As more data is gathered, with the amount of data doubling every three years, data mining is becoming an increasingly important tool to transform this data into information....
, and bioinformatics
Bioinformatics

Bioinformatics is the application of information technology to the field of molecular biology. The term bioinformatics was coined by Paulien Hogeweg in 1978 for the study of informatic processes in biotic systems....
, fluid dynamics
Fluid dynamics

In physics, fluid dynamics is the sub-discipline of fluid mechanics dealing with fluid flow — the natural science of fluids in motion....
, and many other areas. Such software relies heavily on the development, analysis, and implementation of state-of-the-art algorithms for solving various numerical linear algebra problems, in large part because of the role of matrices in finite difference
Finite difference method

In mathematics, finite-difference methods are numerical methods for approximating the solutions to differential equations using finite difference equations to approximate derivatives....
 and finite element method
Finite element method

The finite element method is a numerical analysis for finding approximate solutions of partial differential equations as well as of integral equations....
s.

Common problems in numerical linear algebra include computing the following: LU decomposition
LU decomposition

In linear algebra, the LU decomposition is a matrix decomposition which writes a matrix as the product of a lower triangular matrix and an upper triangular matrix....
, QR decomposition
QR decomposition

In linear algebra, the QR decomposition of a matrix is a matrix decomposition of the matrix into an orthogonal matrix and a right triangular matrix....
, Singular value decomposition
Singular value decomposition

In linear algebra, the singular value decomposition is an important Matrix decomposition of a rectangular real number or complex number matrix , with several applications in signal processing and statistics....
, eigenvalues.








Discussion
Ask a question about 'Numerical linear algebra'
Start a new discussion about 'Numerical linear algebra'
Answer questions from other users
Full Discussion Forum



Encyclopedia


Numerical linear algebra is the study of algorithms for performing linear algebra
Linear algebra

Linear algebra is the branch of mathematics concerned with the study of Euclidean vectors, vector spaces , linear maps , and system of linear equations....
 computations, most notably matrix
Matrix (mathematics)

In mathematics, a matrix is a rectangular array of numbers, as shown at the right. In addition to a number of elementary, entrywise operations such as matrix addition a key notion is matrix multiplication....
 operations, on computer
Computer

A computer is a machine that manipulates Data according to a list of Code .The first devices that resemble modern computers date to the mid-20th century , although the computer concept and various machines similar to computers existed earlier....
s. It is often a fundamental part of engineering
Engineering

Engineering is the discipline and profession of applying Technology and science knowledge and utilizing natural laws and physical resources in order to design and implement materials, structures, machines, devices, systems, and process that safely realize a desired objective and meet specified criteria....
 and computational science
Computational science

Computational science is the field of study concerned with constructing mathematical models and numerical solution techniques and using computers to analyse and solve scientific, social science and engineering problems....
 problems, such as image
Image processing

In electrical engineering and computer science, image processing is any form of signal processing for which the input is an , such as photographs or video frame; the output of image processing can be either an image or a set of characteristics or parameters related to the image....
 and signal processing
Signal processing

Signal processing is the analysis, interpretation, and manipulation of signal . Signals of interest include: audio signal processing, , time-varying measurement values and sensor data, for example biological data such as electrocardiograms, control system signals, telecommunication transmission signals such as radio signals, and many others....
, computational finance
Computational finance

Computational finance or financial engineering is a cross-disciplinary field which relies on computational intelligence, mathematical finance, Numerical analysis and computer simulations to make Trader , hedge and investment decisions, as well as facilitating the risk management of those decisions....
, materials science
Materials science

Materials science or materials engineering is an interdisciplinary field involving the properties of matter and its applications to various areas of science and engineering....
 simulations, structural biology
Structural biology

Structural biology is a branch of molecular biology, biochemistry, and biophysics concerned with the molecular structure of biological macromolecules, especially proteins and nucleic acids, how they acquire the structures they have, and how alterations in their structures affect their function....
, data mining
Data mining

Data mining is the process of extracting hidden patterns from data. As more data is gathered, with the amount of data doubling every three years, data mining is becoming an increasingly important tool to transform this data into information....
, and bioinformatics
Bioinformatics

Bioinformatics is the application of information technology to the field of molecular biology. The term bioinformatics was coined by Paulien Hogeweg in 1978 for the study of informatic processes in biotic systems....
, fluid dynamics
Fluid dynamics

In physics, fluid dynamics is the sub-discipline of fluid mechanics dealing with fluid flow — the natural science of fluids in motion....
, and many other areas. Such software relies heavily on the development, analysis, and implementation of state-of-the-art algorithms for solving various numerical linear algebra problems, in large part because of the role of matrices in finite difference
Finite difference method

In mathematics, finite-difference methods are numerical methods for approximating the solutions to differential equations using finite difference equations to approximate derivatives....
 and finite element method
Finite element method

The finite element method is a numerical analysis for finding approximate solutions of partial differential equations as well as of integral equations....
s.

Common problems in numerical linear algebra include computing the following: LU decomposition
LU decomposition

In linear algebra, the LU decomposition is a matrix decomposition which writes a matrix as the product of a lower triangular matrix and an upper triangular matrix....
, QR decomposition
QR decomposition

In linear algebra, the QR decomposition of a matrix is a matrix decomposition of the matrix into an orthogonal matrix and a right triangular matrix....
, Singular value decomposition
Singular value decomposition

In linear algebra, the singular value decomposition is an important Matrix decomposition of a rectangular real number or complex number matrix , with several applications in signal processing and statistics....
, eigenvalues.

See also

  • Numerical analysis
    Numerical analysis

    Numerical analysis is the study of algorithms for the problems of continuous mathematics .One of the earliest mathematical writings is the Babylonian tablet YBC 7289, which gives a sexagesimal numerical approximation of , the length of the diagonal in a unit square....
    , of which numerical linear algebra is a subspecialty
  • Gaussian elimination
    Gaussian elimination

    In linear algebra, Gaussian elimination is an efficient algorithm for solving system of linear equations, finding the Rank of a matrix , and calculating the inverse of an invertible matrix....
    , an important algorithm in numerical linear algebra
  • BLAS and LAPACK
    LAPACK

    LAPACK, the Linear Algebra PACKage, is a software library for numerical computation originally written in Fortran and now written in Fortran....
    , highly optimized computer libraries which implement most basic algorithms in numerical linear algebra.